Our formulation is based on canonical methods of non-adiabatic quantum
dynamics, used for some time in various fields such as quantum chaos or
quantum chemistry
[1]}, [2]}, [3]}, [4]} mainly for
systems with finitely many classical degrees of freedom. Related methods
[5]}, [6]}, [7]} have been applied recently to spherically
symmetric models of collapsing shells [8]}. Our task will be to
extend these methods to quantum field theories, and to incorporate access to
space-time structure so as to make sure that they are generally covariant. In
particular, we will consider a generalization of quasiclassical methods to
constrained systems, applied to the Hamiltonian and diffeomorphism constraints
of canonical general relativity. By requiring that quantum-corrected
constraints obey suitable Poisson brackets known from hypersurface
deformations [9]}, [10]}, [11]}, we will show that they generate
gauge transformations consistent with the existence of a line element as the
basis for a geometrical interpretation of the theory.
